In this paper, a manufacturing system composed by a single machine, a buffer and a stochastic demand is considered. A discrete flow model is adopted to describe the system and to take into account delivery times. The goal of this paper is to evaluate the optimal buffer level, based on a hedging point policy. This optimal buffer allows minimising the total cost which is the sum of inventory, transportation and lost sales costs. Infinitesimal perturbation analysis is proposed for optimisation of the failure-prone manufacturing system. Indeed, based on discrete flow model, trajectories of all variables are studied and the perturbation analysis estimates are evaluated. These estimates are shown to be unbiased and then are implanted in an optimisation algorithm which determines the optimal buffer level in the presence of delivery time.
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Turki et al. (2012) studied this question.